Abstract : The analysis was begun with an investigation of the effect that a more accurate displacement assumption, in conjunction with the exact strain-displacement relations, has on the postbuckling equilibrium behavior. It was hoped that the limiting behavior of wall thickness and wave number parameter would be altered, and that the stress coefficient would not tend to zero. Particular attention was given to an exact representation of membrane strains because it was known that in the limit as the radius-to-thickness ratio of the shell approaches infinity, the displacements approach the inextensional polyhedral surface. While all the strains in the middle surface of this limiting polyhedral shell are zero, the Donnell strain-displacement relations yield strains amounting to 0.1% if the number of waves around the circumference is 10. The results obtained did not differ significantly from the Donnell strain-displacement relations. (Author)